Why Doesn't the Sun's Core Contain Heavy Metals Like Earth's Core?

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Television shows about astronomy explain the formation of our solar system as a result of remnants of a supernova. Gravity pulled everything together to form our sun and planets. The explanation given for the sun to shine was that hydrogen atoms at the core were being fused together to create helium. I hope I'm correct so far.

At the same time the planets were forming including Earth. The explanation why the Earth is hot is due to fission of heavy metals at its core.

My question is why doesn't the sun have heavy metals at its core like the Earth? And if it does why isn't fission ever mentioned?

Another question I have is: During the formation of the solar system wouldn't it be logical that the heaviest elements would end up at the center of the solar system that is the core of the sun?
 
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My question is why doesn't the sun have heavy metals at its core like the Earth?
It does. They are most likely not forming a iron-nickel core, though, it's not the environment for such a thing.
And if it does why isn't fission ever mentioned?
It's insignificant compared to the fusion power.
During the formation of the solar system wouldn't it be logical that the heaviest elements would end up at the center of the solar system that is the core of the sun?
It would be logical that you find more heavy elements the nearer you are at the center. But that's a general trend only, the elements are not cleanly separated by atomic weight. Too much turbulence, heat, solidity, and everything went too quick.
 
leonstavros said:
Another question I have is: During the formation of the solar system wouldn't it be logical that the heaviest elements would end up at the center of the solar system that is the core of the sun?
That is not what theory says and it is not what observations of the sun tell us about the composition of the sun. Think of it this way: Carbon dioxide is considerably more dense than nitrogen and oxygen, and yet the CO2 in the atmosphere does not fall to the bottom of the atmosphere and form a suffocating three meter thick layer of pure CO2. Instead, that CO2 is pretty well dispersed throughout the atmosphere.

The high temperatures, turbulence, and convection in a protostar would have made the initial protosun have a rather uniform makeup throughout: 72 percent hydrogen, 26 percent helium, and 2 percent heavier elements (and almost all of that 2% is carbon and oxygen). Thanks to fusion, the Sun's core is now somewhat depleted of hydrogen. Just as earthquakes give a window into the Earth's core, vibrations in the sun give a clue as to the makeup of the Sun's interior. That picture is consistent with theory: Hydrogen (depleted compared to the outer parts of the Sun), helium (enriched compared to the outer parts of the Sun), and 2% other stuff, most of which is carbon and oxygen.
 
See http://atropos.as.arizona.edu/aiz/teaching/nats102/mario/solar_system.html for discussion of elemental abundances in the solar system. The sun, while predominately composed of hydrogen and helium, still has a respectable amount of heavier elements in the mix. The percentages look small, but, the totals far exceed that of all the planets combined. The heavy elements in the sun are more diffusely distributed than on Earth for reasons already noted.
 

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